What about the visor test? Did you try it?

If it works, it is an even lower cost way - uh, free... to rule out the Ignition switch..

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'99 E39 528i 5-speed 130k
'06 325Cic auto 115k
'05 X5 3.0 auto 173k-SOLD
'03 530i - manual swapped - 430k miles-SOLD